The homotopy type of the space of algebraic loops on a toric variety

TL;DR

This paper studies the homotopy properties of algebraic loop spaces on toric varieties, establishing stability results by combining spectral sequences and scanning maps to understand their topological structure.

Contribution

It introduces a homotopy stability theorem for algebraic loops on toric varieties using spectral sequences and scanning maps, advancing the understanding of their topological behavior.

Findings

Proves a homotopy stability result for algebraic loop spaces on toric varieties.

Uses Vassiliev spectral sequence and scanning map techniques.

Provides new insights into the topology of algebraic loops on toric varieties.

Abstract

We investigate the homotopy type of the space of tuples of polynomials inducing base-point preserving algebraic maps from the circle S1 to a toric variety X{\Sigma}. In particular, we prove a homotopy stability result for this space by combining the Vassiliev spectral sequence and the scanning map.